PM Review — Rational Numbers

Question 1 Difficulty 1

What is the ratio of 2 to 5 represented as a fraction?

A 2/5
B 5/2
C 1/2
D 2/7

💡 Explanation The ratio of 2 to 5 can be represented as the fraction 2/5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 2 Difficulty 1

If the ratio of apples to oranges is 4:1, how many oranges are there if there are 16 apples?

A 4
B 1
C 16
D 8

💡 Explanation Using the ratio 4:1, if there are 16 apples, then there are 16/4 = 4 oranges.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 3 Difficulty 1

Which of the following represents a part-to-whole ratio?

A 3:2
B 3:5
C 4:6
D 2:7

💡 Explanation A part-to-whole ratio compares a part to the total, thus 3:5 is a part-to-whole ratio.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 4 Difficulty 1

Which of the following ratios is equivalent to 6:9?

A 2:3
B 3:2
C 6:12
D 9:3

💡 Explanation Dividing both parts of 6:9 by 3 gives 2:3, which is equivalent.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 5 Difficulty 1

If the ratio of boys to girls in a class is 2:3, how many boys are there if there are 15 girls?

A 10
B 6
C 12
D 9

💡 Explanation From the ratio 2:3, for every 3 girls, there are 2 boys. If there are 15 girls, (15 * 2)/3 = 10 boys.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 6 Difficulty 1

What is the ratio of 10 to 25 simplified?

A 2:5
B 5:10
C 1:2
D 10:25

💡 Explanation 10 and 25 can be simplified by dividing both by 5, yielding 2:5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 7 Difficulty 1

If the ratio of cats to dogs is 5:2, how many dogs are there when there are 25 cats?

A 10
B 12
C 5
D 2

💡 Explanation Using the ratio 5:2, if there are 25 cats, then (25 * 2)/5 = 10 dogs.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 8 Difficulty 1

Which of the following ratios is not equivalent to 4:8?

A 1:2
B 2:4
C 3:6
D 4:8

💡 Explanation The ratio 3:6 simplifies to 1:2, while 4:8 simplifies to 1:2, but 3:6 is not equivalent to 4:8.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 9 Difficulty 1

If there are 8 red balls and 4 blue balls, what is the ratio of red balls to blue balls?

A 8:4
B 2:1
C 4:2
D 1:2

💡 Explanation The ratio 8:4 simplifies to 2:1 by dividing both parts by 4.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 10 Difficulty 1

What is the ratio of 12 to 36 in simplest form?

A 1:3
B 3:1
C 2:1
D 4:1

💡 Explanation Dividing both numbers by 12 gives the simplest form of 1:3.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 11 Difficulty 2

A recipe requires 2 cups of sugar and 3 cups of flour. What is the ratio of sugar to flour?

A 3:2
B 2:3
C 5:3
D 3:5

💡 Explanation The ratio of sugar to flour is expressed as 2:3 based on the given quantities.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 12 Difficulty 2

If the ratio of length to width of a rectangle is 5:3 and the length is 15 cm, what is the width?

A 9 cm
B 7 cm
C 10 cm
D 5 cm

💡 Explanation Using the ratio 5:3, width = (3/5) * 15 = 9 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 13 Difficulty 2

In a survey, 10 students preferred math and 20 preferred science. What is the part-to-part ratio of students preferring math to those preferring science?

A 1:2
B 2:1
C 3:1
D 1:3

💡 Explanation The part-to-part ratio of students preferring math to science is 10:20, which simplifies to 1:2.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 14 Difficulty 2

If a class has 12 boys and 18 girls, what is the part-to-whole ratio of boys to the total number of students?

A 2:5
B 5:2
C 12:30
D 1:3

💡 Explanation The total number of students is 30, thus the ratio of boys to total students is 12:30, simplifying to 2:5.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 15 Difficulty 2

A car travels 60 km in 1 hour and 90 km in 1.5 hours. What is the ratio of distance to time?

A 4:3
B 3:2
C 2:1
D 5:4

💡 Explanation Distance to time for the two instances is 60:1 and 90:1.5, which both yield a ratio of 4:3 when simplified.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 16 Difficulty 2

If a fruit basket contains 5 apples, 3 bananas, and 2 oranges, what is the ratio of bananas to total fruits?

A 1:10
B 3:10
C 3:5
D 2:5

💡 Explanation The total number of fruits is 10, so the ratio of bananas to total fruits is 3:10.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 17 Difficulty 2

In a class, the ratio of boys to girls is 4:5. If there are 36 students in total, how many boys are there?

A 16
B 20
C 18
D 14

💡 Explanation The total parts are 4 + 5 = 9. Thus, the number of boys = (4/9) * 36 = 16.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 18 Difficulty 2

A recipe calls for a ratio of 3:2 for flour and sugar. If you have 12 cups of flour, how much sugar is needed?

A 8 cups
B 6 cups
C 4 cups
D 10 cups

💡 Explanation Using the ratio 3:2, if 12 cups of flour are used, then sugar needed = (2/3) * 12 = 8 cups.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 19 Difficulty 2

If the ratio of two numbers is 7:2, what is the larger number if the sum is 90?

A 70
B 30
C 40
D 20

💡 Explanation Let the numbers be 7x and 2x. Therefore, 7x + 2x = 90 implies 9x = 90, thus x = 10 and the larger number is 7x = 70.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 20 Difficulty 2

In a class of 30 students, the ratio of boys to girls is 1:2. How many boys are there?

A 10
B 15
C 20
D 5

💡 Explanation The total parts are 1 + 2 = 3. Thus, the number of boys = (1/3) * 30 = 10.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 21 Difficulty 3

If the ratio of boys to girls is 3:4, and there are 21 boys, how many girls are there?

A 24
B 28
C 18
D 30

💡 Explanation Using the ratio 3:4, if there are 21 boys, then the number of girls is (4/3) * 21 = 28.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 22 Difficulty 3

A map has a scale of 1:100000. If the distance between two towns on the map is 5 cm, what is the actual distance?

A 5 km
B 10 km
C 15 km
D 20 km

💡 Explanation The actual distance is 5 cm * 100000 cm = 500000 cm = 5 km.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 23 Difficulty 3

In a class, the ratio of students who like math to those who like science is 2:3. If 30 students like math, how many like science?

A 45
B 60
C 50
D 30

💡 Explanation Using the ratio 2:3, if 30 students like math, then (3/2) * 30 = 45 students like science.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 24 Difficulty 3

If the ratio of a rectangle’s width to its length is 1:4 and the width is 5 cm, what is the length?

A 10 cm
B 15 cm
C 20 cm
D 25 cm

💡 Explanation Using the ratio 1:4, if width = 5 cm, then length = 5 * 4 = 20 cm.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 25 Difficulty 3

A family has a ratio of 2 adults to 3 children. If they have 18 children, how many adults do they have?

A 12
B 10
C 8
D 6

💡 Explanation Using the ratio 2:3, with 18 children, the number of adults = (2/3) * 18 = 12.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 26 Difficulty 3

If a recipe requires a ratio of 4:5 for flour to sugar, how much sugar is needed if 8 cups of flour are used?

A 10 cups
B 12 cups
C 14 cups
D 16 cups

💡 Explanation Using the ratio 4:5, if flour = 8 cups, then sugar needed = (5/4) * 8 = 10 cups.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 27 Difficulty 3

In a class of 40 students, the ratio of boys to girls is 3:5. How many boys are there?

A 15
B 20
C 24
D 30

💡 Explanation The total parts are 3 + 5 = 8. Thus, the number of boys = (3/8) * 40 = 15.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 28 Difficulty 3

A car traveled 240 km in 3 hours. What is the ratio of distance to time?

A 80:1
B 70:1
C 60:1
D 50:1

💡 Explanation The ratio of distance to time is 240 km:3 hours, simplifying to 80:1.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 29 Difficulty 3

In a fruit basket, the ratio of apples to oranges is 3:2. If there are 30 fruits in total, how many apples are there?

A 18
B 12
C 15
D 9

💡 Explanation The total parts are 3 + 2 = 5. Thus, the number of apples = (3/5) * 30 = 18.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 30 Difficulty 3

If the ratio of two numbers is 5:7 and their sum is 96, what is the larger number?

A 56
B 40
C 48
D 36

💡 Explanation Let the numbers be 5x and 7x. Therefore, 5x + 7x = 96 implies 12x = 96, thus x = 8 and the larger number is 7x = 56.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 31 Difficulty 4

If the ratio of boys to girls is 3:5 and there are 45 boys, what is the total number of girls?

A 75
B 90
C 60
D 100

💡 Explanation Using the ratio 3:5, if there are 45 boys, the total number of girls is (5/3) * 45 = 75.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 32 Difficulty 4

A recipe requires a ratio of 2:3 for flour to sugar and you have 12 cups of sugar. How much flour is needed to maintain the ratio?

A 8 cups
B 6 cups
C 10 cups
D 4 cups

💡 Explanation Using the ratio 2:3, if sugar = 12 cups, then flour needed = (2/3) * 12 = 8 cups.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 33 Difficulty 4

If a class has a ratio of boys to girls as 4:5 and there are 72 students total, how many boys are there?

A 32
B 40
C 36
D 48

💡 Explanation The total parts are 4 + 5 = 9. Thus, the number of boys = (4/9) * 72 = 32.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 34 Difficulty 4

In a class of 60 students, the ratio of boys to girls is 1:2. How many girls are there if 15 boys are added?

A 45
B 30
C 40
D 50

💡 Explanation Initially, the number of boys = (1/3) * 60 = 20. After adding 15 boys, there are 35 boys, making girls = 60 - 35 = 25.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 35 Difficulty 4

If the ratio of two numbers is 2:3, and their sum is 40, what are the two numbers?

A 16 and 24
B 20 and 30
C 12 and 18
D 8 and 12

💡 Explanation Let the two numbers be 2x and 3x. Thus, 2x + 3x = 40, leading to 5x = 40 and x = 8. The numbers are 2(8) = 16 and 3(8) = 24.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 36 Difficulty 4

If the ratio of two variables x and y is 5:3, and x = 25, what is the value of y?

A 12
B 15
C 20
D 10

💡 Explanation Using the ratio 5:3, if x = 25, then y = (3/5) * 25 = 15.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 37 Difficulty 4

In a fruit basket, the ratio of apples to bananas is 3:2. If there are 30 fruits total, how many apples are there?

A 18
B 12
C 15
D 10

💡 Explanation The total parts are 3 + 2 = 5. Thus, the number of apples = (3/5) * 30 = 18.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 38 Difficulty 4

If a class has a ratio of boys to girls as 3:4 and there are 42 students total, how many girls are there?

A 24
B 18
C 20
D 21

💡 Explanation The total parts are 3 + 4 = 7. Thus, the number of girls = (4/7) * 42 = 24.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 39 Difficulty 4

A car travels 180 km in 2 hours. What is the ratio of distance to time?

A 90:1
B 80:1
C 70:1
D 60:1

💡 Explanation The ratio of distance to time is 180 km:2 hours, simplifying to 90:1.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?

Question 40 Difficulty 4

If the ratio of boys to girls is 4:5 and there are 36 boys, what is the total number of students?

A 81
B 72
C 90
D 100

💡 Explanation Using the ratio 4:5, if there are 36 boys, then the total students = (9/4) * 36 = 81.

Thought Direction Does it guide toward the right thinking?

Playfulness Is it engaging and fun?

Guidance Quality How well does it scaffold learning?

Curiosity Building Does it spark wonder?